Abstract:A classic problem in Ramsey theory is determining, for a given graph G, the largest value of n such that there exist an edge coloring of the complete graph on n vertices that does not contain a monochromatic subgraph that is isomorphic to G. This talk will discuss, asymptotically, how many monochromatic copies of G must exist in an edge coloring of the complete graph on n vertices. This value is known as the Ramsey Multiplicity. A graph is rainbow if each edge of the graph is distinctly colored. We will also discuss Anti-Ramsey Multiplicities, which is the asymptotic maximum number of rainbow copies of a graph G that can exist in an edge coloring of the complete graph on n vertices.